Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells

Abstract: We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to $f$-wave pairing of composite fermions. This state is topologically distinct from the familiar $p$-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.